Even Mathieu function: Series representations (formula 11.01.06.0006)

MathieuC

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuC[a,q,z]

Series representations

Generalized power series

Expansions at q==0

http://functions.wolfram.com/11.01.06.0006.01

Input Form

MathieuC[MathieuCharacteristicA[2, q], q, z] \[Proportional] SeriesData[$CellContext`q, 0, {Cos[$CellContext`z], Rational[-1, 8] Cos[3 $CellContext`z], Rational[-1, 128] Cos[$CellContext`z] + Rational[-1, 64] Cos[3 $CellContext`z] + Rational[1, 192] Cos[5 $CellContext`z], Rational[-1, 512] Cos[$CellContext`z] + Rational[1, 3072] Cos[3 $CellContext`z] + Rational[1, 1152] Cos[5 $CellContext`z] + Rational[-1, 9216] Cos[7 $CellContext`z], Rational[-37, 294912] Cos[$CellContext`z] + Rational[49, 73728] Cos[3 $CellContext`z] + Rational[-1, 49152] Cos[7 $CellContext`z] + Rational[1, 737280] Cos[9 $CellContext`z], Rational[121, 1769472] Cos[$CellContext`z] + Rational[317, 2359296] Cos[3 $CellContext`z] + Rational[-41, 1179648] Cos[5 $CellContext`z] + Rational[-1, 5898240] Cos[7 $CellContext`z] + Rational[1, 3686400] Cos[9 $CellContext`z] + Rational[-1, 88473600] Cos[11 $CellContext`z], Rational[8105, 339738624] Cos[$CellContext`z] + Rational[-103, 56623104] Cos[3 $CellContext`z] + Rational[-731, 94371840] Cos[5 $CellContext`z] + Rational[379, 471859200] Cos[7 $CellContext`z] + Rational[1, 283115520] Cos[9 $CellContext`z] + Rational[-1, 424673280] Cos[11 $CellContext`z] + Rational[1, 14863564800] Cos[13 $CellContext`z], Rational[481, 226492416] Cos[$CellContext`z] + Rational[-102547, 13589544960] Cos[3 $CellContext`z] + Rational[-659, 11324620800] Cos[5 $CellContext`z] + Rational[12677, 67947724800] Cos[7 $CellContext`z] + Rational[-181, 16986931200] Cos[9 $CellContext`z] + Rational[-1, 26424115200] Cos[11 $CellContext`z] + Rational[1, 69363302400] Cos[13 $CellContext`z] + Rational[-1, 3329438515200] Cos[15 $CellContext`z], Rational[-1237783, 1449551462400] Cos[$CellContext`z] + Rational[-940781, 543581798400] Cos[3 $CellContext`z] + Rational[322897, 815372697600] Cos[5 $CellContext`z] + Rational[9413, 3261490790400] Cos[7 $CellContext`z] + Rational[-2143, 845571686400] Cos[9 $CellContext`z] + Rational[1229, 13317754060800] Cos[11 $CellContext`z] + Rational[1, 3805072588800] Cos[13 $CellContext`z] + Rational[-1, 15220290355200] Cos[15 $CellContext`z] + Rational[1, 958878292377600] Cos[17 $CellContext`z], Rational[-11221967, 32614907904000] Cos[$CellContext`z] + Rational[506831, 104367705292800] Cos[3 $CellContext`z] + Rational[310133, 3131031158784] Cos[5 $CellContext`z] + Rational[-5039101, 547930452787200] Cos[7 $CellContext`z] + Rational[-16013, 319626097459200] Cos[9 $CellContext`z] + Rational[3167, 142056043315200] Cos[11 $CellContext`z] + Rational[-481, 852336259891200] Cos[13 $CellContext`z] + Rational[-1, 767102633902080] Cos[15 $CellContext`z] + Rational[1, 4314952315699200] Cos[17 $CellContext`z] + Rational[-1, 345196185255936000] Cos[19 $CellContext`z], Rational[-4539285691, 125241246351360000] Cos[$CellContext`z] + Rational[1282939901, 12524124635136000] Cos[3 $CellContext`z] + Rational[10304813, 5844591496396800] Cos[5 $CellContext`z] + Rational[-48740801, 20456070237388800] Cos[7 $CellContext`z] + Rational[7516703, 61368210712166400] Cos[9 $CellContext`z] + Rational[30773, 61368210712166400] Cos[11 $CellContext`z] + Rational[-25379, 184104632136499200] Cos[13 $CellContext`z] + Rational[2839, 1104627792818995200] Cos[15 $CellContext`z] + Rational[1, 204560702373888000] Cos[17 $CellContext`z] + Rational[-1, 1534205267804160000] Cos[19 $CellContext`z] + Rational[1, 151886321512611840000] Cos[21 $CellContext`z]}, 0, 11, 1]

Standard Form

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"4608"], "-", FractionBox[RowBox[List["Cos", "[", RowBox[List["8", " ", "z"]], "]"]], "23040"]]], ")"]], " ", SuperscriptBox["q", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["51191", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "2654208"], "-", FractionBox[RowBox[List["29", " ", RowBox[List["Cos", "[", RowBox[List["6", " ", "z"]], "]"]]]], "737280"], "+", FractionBox[RowBox[List["Cos", "[", RowBox[List["10", " ", "z"]], "]"]], "2211840"]]], ")"]], " ", SuperscriptBox["q", "4"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["134855", "10616832"], "-", FractionBox[RowBox[List["181193", " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "z"]], "]"]]]], "159252480"], "+", FractionBox[RowBox[List["23", " ", RowBox[List["Cos", "[", RowBox[List["8", " ", "z"]], "]"]]]], "66355200"], "-", FractionBox[RowBox[List["Cos", "[", RowBox[List["12", " ", "z"]], "]"]], "309657600"]]], ")"]], " ", SuperscriptBox["q", "5"]]], "+", 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RowBox[List["Cos", "[", RowBox[List["10", " ", "z"]], "]"]]]], "16569416892284928000"], "+", FractionBox[RowBox[List["13981", " ", RowBox[List["Cos", "[", RowBox[List["14", " ", "z"]], "]"]]]], "87668872445952000"], "+", FractionBox[RowBox[List["73", " ", RowBox[List["Cos", "[", RowBox[List["18", " ", "z"]], "]"]]]], "75943160756305920000"], "+", FractionBox[RowBox[List["Cos", "[", RowBox[List["22", " ", "z"]], "]"]], "911317929075671040000"]]], ")"]], " ", SuperscriptBox["q", "10"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "11"], SeriesData[$CellContext`q, 0, List[], 0, 11, 1]]]], SeriesData[$CellContext`q, 0, List[Cos[$CellContext`z], Times[Rational[-1, 8], Cos[Times[3, $CellContext`z]]], Plus[Times[Rational[-1, 128], Cos[$CellContext`z]], Times[Rational[-1, 64], Cos[Times[3, $CellContext`z]]], Times[Rational[1, 192], Cos[Times[5, $CellContext`z]]]], Plus[Times[Rational[-1, 512], Cos[$CellContext`z]], Times[Rational[1, 3072], Cos[Times[3, $CellContext`z]]], Times[Rational[1, 1152], Cos[Times[5, $CellContext`z]]], Times[Rational[-1, 9216], Cos[Times[7, $CellContext`z]]]], Plus[Times[Rational[-37, 294912], Cos[$CellContext`z]], Times[Rational[49, 73728], Cos[Times[3, $CellContext`z]]], Times[Rational[-1, 49152], Cos[Times[7, $CellContext`z]]], Times[Rational[1, 737280], Cos[Times[9, $CellContext`z]]]], Plus[Times[Rational[121, 1769472], Cos[$CellContext`z]], Times[Rational[317, 2359296], Cos[Times[3, $CellContext`z]]], Times[Rational[-41, 1179648], Cos[Times[5, $CellContext`z]]], Times[Rational[-1, 5898240], Cos[Times[7, $CellContext`z]]], Times[Rational[1, 3686400], Cos[Times[9, $CellContext`z]]], Times[Rational[-1, 88473600], Cos[Times[11, $CellContext`z]]]], Plus[Times[Rational[8105, 339738624], Cos[$CellContext`z]], Times[Rational[-103, 56623104], Cos[Times[3, $CellContext`z]]], Times[Rational[-731, 94371840], Cos[Times[5, $CellContext`z]]], Times[Rational[379, 471859200], Cos[Times[7, $CellContext`z]]], Times[Rational[1, 283115520], Cos[Times[9, $CellContext`z]]], Times[Rational[-1, 424673280], Cos[Times[11, $CellContext`z]]], Times[Rational[1, 14863564800], Cos[Times[13, $CellContext`z]]]], Plus[Times[Rational[481, 226492416], Cos[$CellContext`z]], Times[Rational[-102547, 13589544960], Cos[Times[3, $CellContext`z]]], Times[Rational[-659, 11324620800], Cos[Times[5, $CellContext`z]]], Times[Rational[12677, 67947724800], Cos[Times[7, $CellContext`z]]], Times[Rational[-181, 16986931200], Cos[Times[9, $CellContext`z]]], Times[Rational[-1, 26424115200], Cos[Times[11, $CellContext`z]]], Times[Rational[1, 69363302400], Cos[Times[13, $CellContext`z]]], Times[Rational[-1, 3329438515200], Cos[Times[15, $CellContext`z]]]], Plus[Times[Rational[-1237783, 1449551462400], Cos[$CellContext`z]], Times[Rational[-940781, 543581798400], Cos[Times[3, $CellContext`z]]], Times[Rational[322897, 815372697600], Cos[Times[5, $CellContext`z]]], Times[Rational[9413, 3261490790400], Cos[Times[7, $CellContext`z]]], Times[Rational[-2143, 845571686400], Cos[Times[9, $CellContext`z]]], Times[Rational[1229, 13317754060800], Cos[Times[11, $CellContext`z]]], Times[Rational[1, 3805072588800], Cos[Times[13, $CellContext`z]]], Times[Rational[-1, 15220290355200], Cos[Times[15, $CellContext`z]]], Times[Rational[1, 958878292377600], Cos[Times[17, $CellContext`z]]]], Plus[Times[Rational[-11221967, 32614907904000], Cos[$CellContext`z]], Times[Rational[506831, 104367705292800], Cos[Times[3, $CellContext`z]]], Times[Rational[310133, 3131031158784], Cos[Times[5, $CellContext`z]]], Times[Rational[-5039101, 547930452787200], Cos[Times[7, $CellContext`z]]], Times[Rational[-16013, 319626097459200], Cos[Times[9, $CellContext`z]]], Times[Rational[3167, 142056043315200], Cos[Times[11, $CellContext`z]]], Times[Rational[-481, 852336259891200], Cos[Times[13, $CellContext`z]]], Times[Rational[-1, 767102633902080], Cos[Times[15, $CellContext`z]]], Times[Rational[1, 4314952315699200], Cos[Times[17, $CellContext`z]]], Times[Rational[-1, 345196185255936000], Cos[Times[19, $CellContext`z]]]], Plus[Times[Rational[-4539285691, 125241246351360000], Cos[$CellContext`z]], Times[Rational[1282939901, 12524124635136000], Cos[Times[3, $CellContext`z]]], Times[Rational[10304813, 5844591496396800], Cos[Times[5, $CellContext`z]]], Times[Rational[-48740801, 20456070237388800], Cos[Times[7, $CellContext`z]]], Times[Rational[7516703, 61368210712166400], Cos[Times[9, $CellContext`z]]], Times[Rational[30773, 61368210712166400], Cos[Times[11, $CellContext`z]]], Times[Rational[-25379, 184104632136499200], Cos[Times[13, $CellContext`z]]], Times[Rational[2839, 1104627792818995200], Cos[Times[15, $CellContext`z]]], Times[Rational[1, 204560702373888000], Cos[Times[17, $CellContext`z]]], Times[Rational[-1, 1534205267804160000], Cos[Times[19, $CellContext`z]]], Times[Rational[1, 151886321512611840000], Cos[Times[21, $CellContext`z]]]]], 0, 11, 1]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <semantics> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 128 </mn> </mfrac> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 64 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 192 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 512 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3072 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 1152 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 9216 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 37 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 294912 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 49 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 73728 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 49152 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 737280 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 121 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 1769472 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 317 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2359296 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 41 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1179648 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 5898240 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3686400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 88473600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 8105 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 339738624 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 103 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 56623104 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 731 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 94371840 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 379 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 471859200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 283115520 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 424673280 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 14863564800 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 481 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 226492416 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 102547 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 13589544960 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 659 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 11324620800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 12677 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 67947724800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 181 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 16986931200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 26424115200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 69363302400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3329438515200 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1237783 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 1449551462400 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 940781 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 543581798400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 322897 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 815372697600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 9413 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3261490790400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2143 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 845571686400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1229 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 13317754060800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3805072588800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 15220290355200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 958878292377600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 11221967 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 32614907904000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 506831 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 104367705292800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 310133 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3131031158784 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5039101 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 547930452787200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 16013 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 319626097459200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3167 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 142056043315200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 481 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 852336259891200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 767102633902080 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4314952315699200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 345196185255936000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 4539285691 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 125241246351360000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 1282939901 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 12524124635136000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 10304813 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5844591496396800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 48740801 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 20456070237388800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7516703 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 61368210712166400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 30773 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 61368210712166400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 25379 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 184104632136499200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2839 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1104627792818995200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 204560702373888000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 1534205267804160000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 151886321512611840000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <cos /> <ci> $CellContext`z </ci> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 8 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 128 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 64 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 192 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 512 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3072 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1152 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 9216 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -37 <sep /> 294912 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 49 <sep /> 73728 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 49152 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 737280 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 121 <sep /> 1769472 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 317 <sep /> 2359296 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -41 <sep /> 1179648 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 5898240 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3686400 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 88473600 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 8105 <sep /> 339738624 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -103 <sep /> 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Date Added to functions.wolfram.com (modification date)

2001-10-29